In this paper we present a new theory and an algorithm for image segmentation
based on a strength of connectedness between every pair of image elements. The
object definition used in the segmentation algorithm utilizes the notion of iterative
relative fuzzy connectedness, IRFC. In previously published research, the IRFC
theory was developed only for the case when the segmentation was involved with
just two segments, an object and a background, and each of the segments was
indicated by a single seed. Our
theory, which solves a problem of Udupa and Saha, allows simultaneous
segmentation involving an arbitrary number of objects. Moreover, each segment can
be indicated by more than one seed, which is often more natural and easier than a
single seed object identification.

The first iteration step of the IRFC algorithm gives a segmentation known as relative
fuzzy connectedness, RFC, segmentation. Thus, the IRFC technique is an extension
of the RFC method. Although the RFC theory, due to Saha and Udupa,
is developed in the multi object/multi seed framework, the theoretical results presented
here are considerably more delicate in nature and do not use the results
from earlier papers. On the other hand, the earlier theoretical results are immediate consequences
of the results presented here. Moreover, the new framework not only
subsumes previous fuzzy connectedness descriptions but also sheds new light on
them.

We present examples of segmentations obtained via our IRFC based algorithm in
the multi object/multi seed environment, and compare it with the results obtained
with the RFC based algorithm. Our results indicate that, in many situations, IRFC
outperforms RFC, but there also exist instances where the gain in performance is
negligible.